How do you solve #|8x + 8| + 3 = 35#?

Question

Savannah Anderson · Accepted Answer

#x = 3# and #x = -5#

First, by performing the necessary calculations and maintaining the equation's balance, isolate the absolute value term on one side of the equation:

#abs(8x + 8) + 3 - color(red)(3) = 35 - color(red)(3)#

#abs(8x + 8) + 0 = 32#

#abs(8x + 8) = 32#

We must solve the term in the absolute value for both the positive and negative terms because this problem has an absolute value term, and the absolute value function converts a negative or positive number to its positive equivalent. The absolute value is equal to:

First Solution

#8x + 8 = 32#

#8x + 8 - color(red)(8) = 32 - color(red)(8)#

#8x + 0 = 24#

#8x = 24#

#(8x)/color(red)(8) = 24/color(red)(8)#

#(color(red)(cancel(color(black)(8)))x)/color(red)(cancel(color(black)(8))) = 3#

#x = 3#

Option 2)

#8x + 8 = color(red)(-)32#

#8x + 8 - color(red)(8) = -32 - color(red)(8)#

#8x + 0 = -40#

#8x = -40#

#(8x)/color(red)(8) = -40/color(red)(8)#

#(color(red)(cancel(color(black)(8)))x)/color(red)(cancel(color(black)(8))) = -5#

#x = -5#

Isaiah Anthony · Answer

undefined To solve |8x + 8| + 3 = 35, you first subtract 3 from both sides to isolate the absolute value term. This gives you |8x + 8| = 32. Then, you split the equation into two cases: 8x + 8 = 32 and 8x + 8 = -32. Solve each equation separately for x.

For the first case, 8x + 8 = 32, subtract 8 from both sides to get 8x = 24, then divide both sides by 8 to find x = 3.

For the second case, 8x + 8 = -32, subtract 8 from both sides to get 8x = -40, then divide both sides by 8 to find x = -5.

So the solutions are x = 3 and x = -5.